It looks like it could be a triangle strip or fan with an alpha blended texture, stretched in one direction to give the streak-like appearance. With the texture, it may be best to make it yourself. I would make it white with varying levels of alpha on the streaks, so this way you can tint it to different colors on the shader.

Because you're using DirectX9, you would have to update these triangles on the CPU side, generating them where you want that wisp effect to trail.

The bits of fire on the end can be particles generated from the ends of the triangle strip.

geometry with an alpha texture....

What looks like is going on is for each rendered frame, they save the position and orientation of the weapon. With that they save simple quad and have a tiled texture applied. Each new quad would then be connected to the previous quads verts however you want to calculate that and thats probably it. You can write a shader to move the tiled texture so the flames look like they are moving instead of static.

The effect is called "ribbon trail."

ribbon trail